Question: Solve for $x$ : $5x^2 - 40x - 45 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 {-8}x {-9} = 0 $ The coefficient on the $x$ term is $-8$ and the constant term is $-9$ , so we need to find two numbers that add up to $-8$ and multiply to $-9$ The two numbers $-9$ and $1$ satisfy both conditions: $ {-9} + {1} = {-8} $ $ {-9} \times {1} = {-9} $ $(x {-9}) (x + {1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -9) (x + 1) = 0$ $x - 9 = 0$ or $x + 1 = 0$ Thus, $x = 9$ and $x = -1$ are the solutions.